Uniqueness and stability of regional blow-up in a porous-medium equation

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dc.contributor.authorCortázar, C
dc.contributor.authorDel Pino, M
dc.contributor.authorElgueta, M
dc.date.accessioned2025-01-21T01:30:33Z
dc.date.available2025-01-21T01:30:33Z
dc.date.issued2002
dc.description.abstractWe study the blow-up phenomenon for the porous-medium equation in R-N, N greater than or equal to 1,
dc.description.abstractu(t) = Deltau(m) + u(m),
dc.description.abstractm > 1, for nonnegative, compactly supported initial data. A solution u(x, t) to this problem blows-up at a finite time (T) over bar > 0. Our main result asserts that there is a finite number of points x(1), ..., x(k) is an element of R-N, with \x(i) - x(j)\ greater than or equal to, 2R* for i not equal j, such that
dc.description.abstractlim (t-->(T) over bar)((T) over bar - t)(1/m-1)u(t, x) = Sigma(j=1)(k) w(*)(\x - x(j)\).
dc.description.abstractHere w(*)(\x\) is the unique nontrivial, nonnegative compactly supported, radially symmetric solution of the equation Deltaw(m) + w(m) - 1/m-1w = 0 in R-N and R* is the radius of its support. Moreover u(x, t) remains uniformly bounded up to its blow-up time on compact subsets of R-N\boolean ORj=1k (B) over bar (x(j), R*). The question becomes reduced to that of proving that the omega-limit set in the problem v(t) = Deltav(m) + v(m) - 1/m-1v consists of a single point when its initial condition is nonnegative and compactly supported.
dc.fuente.origenWOS
dc.identifier.issn0294-1449
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/96805
dc.identifier.wosidWOS:000179701400007
dc.issue.numero6
dc.language.isoen
dc.pagina.final960
dc.pagina.inicio927
dc.revistaAnnales de l institut henri poincare-analyse non lineaire
dc.rightsacceso restringido
dc.titleUniqueness and stability of regional blow-up in a porous-medium equation
dc.typeartículo
dc.volumen19
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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